437edo - Revision history

ArrowHead294 at 12:40, 21 February 2025

2025-02-21T12:40:03Z

← Older revision		Revision as of 12:40, 21 February 2025
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	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
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	\| {{monzo\| -1385 437 }}		\| {{monzo\| -1385 437 }}
	\| {{mapping\| 437 1385 }}		\| {{mapping\| 437 1385 }}
	\| 0.1114		\| +0.1114
	\| 0.1114		\| 0.1114
	\| 4.06		\| 4.06

Francium: changed EDO intro to ED intro

2025-02-21T06:06:07Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:06, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|437~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Rework

2023-11-03T08:03:31Z

Rework

← Older revision		Revision as of 08:03, 3 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|437}}		{{EDO intro\|437}}
	==Theory==
	~~437et tempers out 4096000/4084101 and~~ [[~~2401/2400~~]] in the 7-limit~~; 25165824/25109315~~, ~~1835008~~/~~1830125, 2621440/2614689,~~ [[~~16384~~/~~16335~~]], ~~151263/151250~~, ~~107495424/107421875~~, [[~~1953125~~/~~1948617~~]], [[3025/3024]], [[41503/41472]], ~~766656~~/~~765625~~, ~~391314/390625, 20614528/20588575~~ and ~~644204~~/~~643125~~ in the 11-limit.		== Theory ==
	===Odd harmonics===		437edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are quite large, giving us the option of treating it as either a full 11-limit temperament, or a 2.9.15.21.13.17 [[subgroup]] temperament.

			Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[2401/2400]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[41503/41472]], [[16384/16335]], and 151263/151250 in the 11-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|437}}		{{Harmonics in equal\|437}}
	===Subsets and supersets===
	437 factors into ~~19 × 23 with its subset edos~~ {{~~EDOs~~\|19, and ~~23}}~~. [[874edo]], which doubles it, gives a good correction to the harmonic 3.		=== Subsets and supersets ===
	==Regular temperament properties==		Since 437 factors into {{factorization\|437}}, 437edo contains [[19edo]] and [[23edo]] as subsets. [[874edo]], which doubles it, gives a good correction to the harmonic 3.

			== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|-1385 437}}		\| {{monzo\| -1385 437 }}
	\|{{~~val~~\|437 1385}}		\| {{mapping\| 437 1385 }}
	\| 0.1114		\| 0.1114
	\| 0.1114		\| 0.1114
	\| 4.06		\| 4.06
	\|}		\|}
	==Scales==
			== Scales ==
	* [[Namo7]]		* [[Namo7]]
	* [[Namo10]]		* [[Namo10]]
	* [[Namo17]]		* [[Namo17]]

Francium: Created page with "{{Infobox ET}} {{EDO intro|437}} ==Theory== 437et tempers out 4096000/4084101 and 2401/2400 in the 7-limit; 25165824/25109315, 1835008/1830125, 2621440/2614689, 16384/16..."

2023-10-04T13:07:28Z

Created page with "{{Infobox ET}} {{EDO intro|437}} ==Theory== 437et tempers out 4096000/4084101 and 2401/2400 in the 7-limit; 25165824/25109315, 1835008/1830125, 2621440/2614689, 16384/16..."

New page

{{Infobox ET}}
{{EDO intro|437}}
==Theory==
437et tempers out 4096000/4084101 and [[2401/2400]] in the 7-limit; 25165824/25109315, 1835008/1830125, 2621440/2614689, [[16384/16335]], 151263/151250, 107495424/107421875, [[1953125/1948617]], [[3025/3024]], [[41503/41472]], 766656/765625, 391314/390625, 20614528/20588575 and 644204/643125 in the 11-limit.
===Odd harmonics===
{{Harmonics in equal|437}}
===Subsets and supersets===
437 factors into 19 × 23 with its subset edos {{EDOs|19, and 23}}. [[874edo]], which doubles it, gives a good correction to the harmonic 3.
==Regular temperament properties==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.9
|{{monzo|-1385 437}}
|{{val|437 1385}}
| 0.1114
| 0.1114
| 4.06
|}
==Scales==
* [[Namo7]]
* [[Namo10]]
* [[Namo17]]